EP1017964A1 - Systeme de determination d'une trajectoire optimale dans un espace multidimensionnel - Google Patents

Systeme de determination d'une trajectoire optimale dans un espace multidimensionnel

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Publication number
EP1017964A1
EP1017964A1 EP98950653A EP98950653A EP1017964A1 EP 1017964 A1 EP1017964 A1 EP 1017964A1 EP 98950653 A EP98950653 A EP 98950653A EP 98950653 A EP98950653 A EP 98950653A EP 1017964 A1 EP1017964 A1 EP 1017964A1
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EP
European Patent Office
Prior art keywords
vehicle
locus
travel path
cost
travel
Prior art date
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EP98950653A
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German (de)
English (en)
Inventor
William Loring Myers
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University Corp for Atmospheric Research UCAR
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University Corp for Atmospheric Research UCAR
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Application filed by University Corp for Atmospheric Research UCAR filed Critical University Corp for Atmospheric Research UCAR
Publication of EP1017964A1 publication Critical patent/EP1017964A1/fr
Withdrawn legal-status Critical Current

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/26—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
    • G01C21/34—Route searching; Route guidance
    • G01C21/3453—Special cost functions, i.e. other than distance or default speed limit of road segments
    • G01C21/3492—Special cost functions, i.e. other than distance or default speed limit of road segments employing speed data or traffic data, e.g. real-time or historical
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/26—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
    • G01C21/34—Route searching; Route guidance
    • G01C21/3453—Special cost functions, i.e. other than distance or default speed limit of road segments
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/0005—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots with arrangements to save energy

Definitions

  • This invention relates to systems for the computation of travel paths and, in particular, to a system that computes a travel path for a vehicle through a multidimensional space, which travel path optimizes the cost of operation of the vehicle according to at least one predetermined vehicle operating criteria.
  • PROBLEM It is a problem to select a cost optimized travel path for a vehicle from an origination point to a destination point in an efficient and automated manner.
  • the selection of a travel path is typically done on a manual basis or on a limited automated basis to optimize the cost of operation of a vehicle based upon a single one of a plurality of vehicle operating criteria which include, but are not limited to: fuel economy, time of travel, safety, and traffic avoidance.
  • vehicle travel path determination systems are unable to consider multidimensional spaces and, in particular, the time varying characteristics of the multidimensional space in computing the travel path.
  • existing vehicle travel path determination systems typically focus on only a single vehicle operating characteristic in computing the travel path, rather than considering the interrelationship of a plurality of the vehicle operating characteristics as well as the time-varying conditions that exist in the multidimensional space.
  • An example of a travel path computation situation entails aircraft operations, wherein an aircraft is the vehicle that must travel from an origination airport to a destination airport, with the flight originating at a first predetermined time and scheduled to arrive at the destination airport at a second predetermined time.
  • a significant cost factor in calculating the flight path for an aircraft is fuel consumption, since the fuel costs of operating an aircraft can be considerable.
  • another contributing cost factor is the avoidance of meteorological hazards to thereby ensure the safety and comfort of the passengers in the aircraft.
  • the calculation of a flight path for commercial airliners is typically done on a predetermined segment basis, wherein the aircraft travel path is represented by a series of piecewise linear flight segments from point to point. Within this sequence of segments, the aircraft can maneuver around meteorological hazards that are encountered and can make minor altitude adjustments in order to avoid significant headwinds which would seriously impact fuel consumption.
  • This flight path determination for aircraft represents a crude cost optimization system, using predetermined flight segments and manually determined course corrections, to account for meteorological hazards as they are encountered by the aircraft, rather than on a precomputed basis. This renders the cost optimization system fairly inefficient, since anticipation of meteorological hazards or other factors in the flight path determination prior to the departure of the aircraft from the origination point could result in a far more efficient operation of the aircraft. Thus, maneuvering around a meteorological hazard can consume far more fuel than anticipating the presence, locus and predicted movement of the meteorological hazard prior to the departure of the aircraft from the origination point.
  • the existing air traffic control system may be significantly revised from the existing detailed control of aircraft operations by the air traffic controllers along the entirety of the flight path to a "gateway" system wherein the air space is divided into a plurality of large volumetric sections, each of which contains entry and exit points through which aircraft must travel.
  • the air traffic control function in this proposed system regulates the sequence in which aircraft pass through these portals in exiting a first air space volumetric section and entering a second air space volumetric section that is juxtaposed to the first air space volumetric section.
  • the aircraft would then have relative freedom in traversing a volumetric section from the entrance portal to the exit portal, and a predetermined flight segment would no longer be a necessity in the operation of the aircraft.
  • the above described problems are solved and a technical advance achieved in the field by the present automated travel path determination system which computes a travel path for a vehicle from an origination point to a destination point based on the operating characteristics of the vehicle as well as phenomena extant in the multidimensional space, which phenomena have an impact on the cost of operation of the vehicle.
  • This vehicle travel path determination system can concurrently consider a plurality of vehicle operating characteristics in selecting the travel path.
  • the travel path is optimized for a weighted selection of a number of cost factors, which weighted selection represents a desired combination of cost factors for the operation of this particular vehicle.
  • This vehicle travel path determination system also considers the time varying nature of the phenomena that exist within the multidimensional space and the impact these time varying phenomena have on the vehicle as it traverses the travel path.
  • the user can vary the initial conditions to ascertain the optimized travel path in the case of interactive initial conditions that effect the cost of the travel path.
  • the present automated vehicle travel path determination system is disclosed as a flight path calculation system for aircraft, although the concepts of this system are applicable to any form of vehicle travel.
  • the operating characteristics of an aircraft which can be considered by the vehicle travel path determination system include, but are not limited to: speed of travel, fuel consumption, passenger safety and comfort, hazard avoidance, restricted air space, operating altitude limitations, and other aircraft traffic.
  • the multidimensional space that is considered in determining the travel path of an aircraft consists of the three dimensional volumetric space through which the aircraft travels from its origination point to its destination point, which space includes the in-airport ground operations prior to takeoff and after landing the aircraft.
  • Another dimension that is of interest in this vehicle travel path computation is the temporal nature of both the three dimensional volumetric space and the vehicle operating characteristics. These time varying factors can either be measured or predicted to thereby enable the vehicle travel path determination system to anticipate their effect on the cost of aircraft operations as the aircraft traverses the multidimensional space.
  • the aircraft operator inputs data to the vehicle travel path determination system indicative of the origination point, destination point, and estimated time of departure.
  • the aircraft operator also indicates the type of aircraft and its operating characteristics, if the aircraft operating characteristics data are not already stored in the system.
  • the aircraft operator can also input data indicative of the various cost factors that are to be considered in the computation of the travel path. These cost factors are typically optimization items such as fuel economy and hazard avoidance.
  • the aircraft operator can also assign weights to these various cost factors to indicate their relative significance to the aircraft operator in computing the travel path.
  • the vehicle travel path determination system itself can consider numerous cost factors which present overriding considerations that cannot be overridden by the aircraft operator.
  • the maximum effective operating altitude can be a significant determining factor in selecting the travel path.
  • the maximum effective altitude of the aircraft In flying through mountainous regions, the maximum effective altitude of the aircraft must be significantly in excess of the height of the mountain peaks, otherwise the small aircraft must be routed around these hazards.
  • the vehicle travel path determination system considers invariant phenomena as well as time varying phenomena in computing the travel path. More subtle factors can also be considered by the vehicle travel path determination system, such as the safety of operating an aircraft in a certain airspace. It is not uncommon for the operator of a small aircraft to be inexperienced and misjudge the dangers of mountain flying.
  • the vehicle travel path determination system may override the aircraft operator travel path selection due to the unreasonable nature of the risks that would be encountered by such an aircraft in using such a travel path.
  • the vehicle travel path determination system therefore considers a plurality of operating characteristics of the vehicle and a plurality of factors that exist in the multidimensional space which can effect the operation of the vehicle, to compute a travel path which represents the optimization of at least one and more likely a plurality of cost factors, which cost factors are weighted in their significance by the aircraft operator.
  • the travel path that is selected by this vehicle travel path determination system represents a sophisticated and user-customizable computation system which takes into account not only time invariant but also time varying phenomena in selecting the travel path.
  • Figure 1 illustrates in block diagram form an overall view of the architecture of the present system for determining the travel path in a multidimensional space
  • Figure 2 illustrates in flow diagram form the operational steps taken by the present system for determining a travel path in a multidimensional space in performing a typical travel path computation
  • Figures 3-7 illustrate in graphical form the implementation of the various steps of the method of operation of Figure 2;
  • Figure 8 illustrates a further application of the present system for determining a travel path in a multidimensional space.
  • the present automated vehicle travel path determination system computes a travel path for a vehicle, which travel path extends from an origination point to a destination point and is determined based on the operating characteristics of the vehicle as well as those phenomena extant in the multidimensional space which have an impact on the cost of operation of the vehicle.
  • This vehicle travel path determination system can concurrently consider a plurality of vehicle operating characteristics in selecting the travel path.
  • the travel path is optimized for a weighted selection of a numberof cost factors, which weighted selection represents a desired combination of cost factors in the vehicle operation.
  • This vehicle travel path determination system also considers the time varying nature of the phenomena that exist within the multidimensional space and the impact these time varying phenomena have on the vehicle as it traverses the travel path.
  • the automated vehicle travel path determination system is disclosed herein as a flight path calculation system for aircraft, although the concepts of this system are applicable to any form of vehicle travel.
  • the vehicle travel path determination system 1 comprises a processor 11 which receives input from at least one and preferably a plurality of sources S1-Sn which sources generate data representative of the nature of the multidimensional space of interest.
  • sources S1-Sn can include sensor based systems that determine the presence, locus and characteristics of various phenomena extant in the multidimensional space.
  • the sources S1-S3 can include, but are not limited to: meteorological monitoring systems S1 , vehicle identification systems S2, topographical representation systems S3, and the like.
  • Each of these sources generates an output which typically comprises a data stream or data file that includes information computed by the source and of interest to the vehicle travel path determination system 1.
  • the sources S1-S3 can include predictive systems Sn, which produce model data indicative of a predicted state of the multidimensional space at some time in the future, which model data may be based upon the data received from the sensor-based sources S1-S3.
  • the model data is generally more valuable to the vehicle travel path determination system 1 than realtime sensor data (non-predictive) if the travel period extends far into the future, since it is the future locus of hazards that are of interest.
  • the data generated by the various sources S1-Sn are transmitted to the vehicle travel path determination system 1 and received therein by the vehicle performance effecting system EF.
  • the data generated by the various sources S1- Sn can be selectively incorporated into the travel path determination process TP, since these sources S1-Sn may generate data which is not considered by the vehicle travel path determination system 1.
  • various thresholds can be established to filter the data generated by the various sources S1-Sn, so that only the data presently pertinent to the travel path determination process TP is considered.
  • all data generated by sources S1-Sn can be received by the vehicle travel path determination system 1 , in which case the vehicle performance effecting system EF represents the component of the travel path determination process TP which characterizes the received data in a manner that converts the raw data into a form which is usable by the travel path determination process TP.
  • a vehicle performance data system VP which functions to identify the operating characteristics of a vehicle V which is extant in the multidimensional space.
  • This vehicle performance data system VP stores data for a plurality of vehicles, which data characterize the operation of the vehicle V. For example, in the aircraft situation, the data can denote: the type of aircraft, maximum speed, maximum altitude, fuel capacity, range of operation, and the like. This data enables the vehicle travel path determination system 1 to compute an optimal travel path as a function of the limitations of the vehicle V which traverses the travel path.
  • an operator performance data system OP which functions to identify the operating characteristics of an operator who operates a vehicle V which is extant in the multidimensional space.
  • This operator performance data system OP stores data for a plurality of operators, which data characterize the limitations of the operator. For example, in the aircraft situation, the data can denote: the type of aircraft which the operator is qualified to operate, the instrument rating of the operator, amount of experience of the operator, aircraft operator's license status, and the like. This data enables the vehicle travel path determination system 1 to compute an optimal travel path for the vehicle V also as a function of the limitations of the operator.
  • the travel path determination process TP represents the algorithmic process, described in additional detail below, which is used by the vehicle travel path determination system 1 to incorporate all of the data provided by the above- noted components, as well as user provided data, to compute a travel path from an origination point to a destination point, which travel path is optimized pursuant to predetermined criteria.
  • the vehicle travel path determination system 1 can also be implemented in whole or in part in the vehicle V itself.
  • the vehicle V itself can include the processor 11 with resident travel path determination process TP and vehicle performance data system VP to thereby perform the necessary computations.
  • the data obtained from sources S1-Sn can be transmitted via radio transmitter T to the vehicle V as the data is available, or as requested by the processor 11 in the vehicle V.
  • the above characterized vehicle travel path determination system 1 operates in general fashion as illustrated in the flow diagram of Figure 2.
  • the user inputs data into vehicle travel path determination system 1 to characterize the desired trip.
  • the user accesses a terminal at step 21 , which terminal is either remotely located from travel path determination system 1 and connected thereto via a communication connection or directly connected thereto.
  • the vehicle travel path determination system 1 at step 22 presents the user with a user interface screen that provides the user with a means of providing the information necessary for the vehicle travel path determination system 1 to perform the desired function.
  • the user must provide data at step 23 which, at a minimum is representative of an origination point, a destination point, a desired time of departure, and identification of the type of aircraft.
  • the data input by the user is stored in memory in the vehicle travel path determination system 1 , which at step 24 queries vehicle performance data system VP and operator performance data system OP to obtain additional information which is required to compute an optimized travel path.
  • the vehicle travel path determination system 1 at step 25 queries vehicle performance effecting system EF to obtain the data which is collected from the various sources S1-Sn.
  • the travel path determination process TP now has sufficient data from which the optimal travel path can be computed.
  • the travel path computation is initiated at step 26 by the travel path determination process TP, which computes the travel path as described below.
  • the computed travel path is then output at step 27 to the user by the vehicle travel path determination system 1.
  • the computed travel path can be retained in memory in the vehicle travel path determination system 1 for future reference, such as to provide dynamic updates.
  • the vehicle travel path determination system 1 can at step 28 automatically, or on a polled basis, recompute the optimal travel path produced at step 26, based upon the present status of the phenomena that are extant in the multidimensional space. This recomputed travel path is then retransmitted to the user at step 27.
  • the recomputed travel path can also be computed locally, on board the aircraft, with only a compact data representation of the meteorological events being uplinked to the aircraft.
  • further optimizations of the travel path can be computed by further optimization iterations.
  • the computational load on the iterative or update processing is greatly reduced from the original travel path computations because a significant portion of the multi-dimensional space is no longer considered, and it is only deviations from the originally computed travel path that are determined. Travel Path Characteristics
  • a travel path through a multidimensional space connects an origination point with a destination point by means of a continuous curve.
  • the continuous curve can be a curvilinear line or it can be a series of linear segments which approximate a continuous curve.
  • the travel path is considered a continuous curve even though it can comprise a plurality of straight line segments, in addition to the travel path being a continuous curve, the curve is a directed curve as shown in Figure 3 in that the vehicle V travels in a predetermined direction along the curve from the originating point to the destination point without retracing a portion of the travel path.
  • the directed curve can be represented as a parameterized function which associates each point (x, y, z) on the curve in the multidimensional space with a time t, with t increasing in value from the start of the directed curve to the end of the directed curve.
  • This parameterized function not only describes the location of the vehicle V in the multidimensional space but also describes the velocity of the vehicle V throughout its travel.
  • the multidimensional space is typically represented by Cartesian coordinates of x, y, and z directions with the x and y axes as shown in Figure 1 defining a horizontally oriented plane throughout the multidimensional space and the z axis representing an azimuthal direction which is perpendicular to the x, y plane. It is obvious that other coordinate systems can be used to represent the multidimensional space and for the purpose of simplicity of description, the Cartesian coordinate system is used herein.
  • a cost function can be associated with any curvilinear parameterized function.
  • the cost function associates the points on the directed curve with a value or a cost at that point.
  • the cost at that point can represent the computation of some value which is indicative of the sum of one or more factors which comprise the cost function.
  • a single value can be obtained which is representative of the cost of a vehicle V traversing the directed path.
  • this cost can take into account a plurality of factors, such as: time expended, environmental hazards encountered, fuel expended, and the like. These factors can be weighted so that the relative importance of each is a measure of their significance to the vehicle operator.
  • the travel path can be represented as the extent of aircraft travel from the origination point to the destination point, which may or may not be inclusive of the travel of the aircraft from its point of loading to the point of takeoff and the point of landing to the point of unloading.
  • the travel path For simplicity of description, consider the travel path to comprise the path from the point of takeoff to the point of landing. Given these constraints, any location in the multidimensional space that is at or below the existing ground surface is obviously considered an unacceptable part of the travel path.
  • the travel path determination system therefore excludes this volumetric space from consideration in determining the travel path.
  • each aircraft has a maximum operating altitude characteristic that delimits the upper bounds of the multidimensional space which must be considered by the travel path determination system for this aircraft.
  • the region outside the extent of space which lies between the origination point and destination point need not be considered in computing the travel path.
  • Additional operating constraints in this environment consist of mandatory minimum altitude requirements for this particular aircraft as well as predefined and mandatory operating rules with regard to aircraft takeoff and landing for noise abatement and hazard avoidance purposes. These constraints must be considered by the system in determining the travel path.
  • the multidimensional space can be viewed as a volumetric region which is occupied by a plurality of phenomena that must be considered in the determination of the travel path for the aircraft.
  • These phenomena can be classified as either immutable or time varying (dynamic).
  • An example of immutable phenomena are regions of restricted air space, such as over a military base or a region of airspace over the territorial extent of unfriendly nations, or the airspace above and around an airport, which airport is not the origination point or destination point.
  • the phenomena that exist within the multidimensional space are typically time varying and more difficult to model and use in the computation of the travel path. These time varying phenomena can include other air traffic and meteorological phenomena.
  • meteorological phenomena loosely defines all atmospheric conditions which can have an effect on the operation of the aircraft in the multidimensional space.
  • Typical examples of meteorological phenomena include: thunderstorms, snow storms, fog, headwinds, temperature conditions and the like.
  • meteorological monitoring systems which use atmospheric models to predict the locus, extent of dynamic regions of meteorological hazard, such as icing conditions or turbulence, which can negatively effect the travel of the aircraft through the regions of the multidimensional space.
  • the degree of severity of these meteorological phenomena in terms of their effect on the aircraft operation can be estimated.
  • Atmospheric models used in the meteorological monitoring system also predict winds throughout the multidimensional space.
  • the horizontal component of these winds is the dominant factor and therefore the vertical component of the winds can be considered negligible unless it exceeds a certain predetermined minimum threshold over which the vertical component significantly effects the aircraft operation.
  • the winds in the multidimensional space typically vary over time, which causes varying effective travel rates for the aircraft along the travel path.
  • head winds are typically experienced at high altitudes while tail winds are often encountered at lower altitudes on a given route.
  • the following example shows a cost function which is a measure of the time from time of travel from the point of origination to the destination point. Infinite penalties are assumed for traversing weather impacted airspace, terrain occupied space or altitudes too high forthe aircraft. The optimal route is therefore the fastest path from the origination point to the destination point.
  • a model of aircraft performance is used which is extremely simple, in that it calculates aircraft direction and speed by the vector addition of the flight direction vector and the wind vector. This simplistic model is used for illustration purposes and a more rigorous model of aircraft performance in various wind conditions would be used to provide increased accuracy of the travel path.
  • the model output is presented on a four-dimensional grid, to enable the system to interpolate the results to any specified time and three- dimensional location in the multi-dimensional space.
  • Travel Path Computation Algorithm There are many potential algorithms that can be used to find an optimal travel path through the multidimensional space. Some of these algorithms attempt to find an analytical solution while others attempt to find a reasonable approximation to an analytical solution. The algorithm selected forthis purpose can find an arbitrarily precise approximation to the true solution. In addition, there are some algorithms which fail to operate properly since they find local minima in a manner similar to the problems encountered while finding global minimum of scalar functions using Newton's method.
  • the graph theory approach uses a directed graph which contains a plurality of nodes and directed edges, where each directed edge connects a pair of the plurality of nodes.
  • the directed edges are used in this approach since the directional travel of the vehicle V is from the origination point to the destination point and the edges which interconnect the nodes therefore need to be directed to ensure forward motion of the vehicle V toward its ultimate destination.
  • a time dependent cost function can be associated with any of the directed edges of this graph. Therefore all the continuous paths which lead from the origination point to the destination point are of interest in performing these computations, and the time that the vehicle V arrives at a particular node is a factor in the computation for the time dependent costs.
  • the graph must be acyclic in order to prevent the cost function computation from traversing the same path segment repeatedly in computing the travel path.
  • the graph network of Figure 4 leads to better results than the graph network of Figure 5, however it requires additional computation complexity to implement.
  • the graph of interconnectivity in the three-dimensional case is given by a single directed edge from every node in slice I to every node in slice 1+1 as shown in Figure 6.
  • This equation seems computationally overwhelming but there are techniques which can bring this number down to a computational order of nx * (ny * nz) 2 . This makes the algorithm practical to use in this particular computation.
  • the technique used is known as a dynamic programming method which computes a least cost to any point in the slice I. Using the costs for that entire slice, the dynamic programming method begins on the next slice by examining all of the paths to a given node.
  • the dynamic programming method then calculates a cost for each of those edges and adds them to the minimal cost for the start nodes of the edges.
  • the initiation of this process is easy since the first slice has nodes whose cost can be determined from the origination point to those nodes.
  • Once the minimum cost on the first slice has been determined it is relatively easy to work forward through the graph to determine the minimum costs at all nodes in the subsequent slices as well as the destination node. Having determined these, it is relatively easy to work back through the graph to determine the travel path giving this minimum cost to any node, in particular, the destination node.
  • the dynamic programming method provides a set of directed edges with coordinates xicide y felicit z, which approximate the optimal route through the multidimensional space.
  • an iterative technique can be used to refine this approximation.
  • the iterative technique is performed in a simplistic manner by moving each point in the y and/or z direction and seeing if the resultant cost is greater or less than before.
  • This multidimensional coordinate system in which the graph is laid out can be assumed to lie along the equator of the globe for computational purposes. By performing rotations on the globe, the origination point and destination point can be brought to lie on the equator with the direction of travel being counterclockwise. In practice, the strip containing the solutions tends to be relatively narrow.
  • X A Aircraft characteristics, including but not limited to: weight, performance, fuel, user preference with respect to tolerable level of turbulence, user preference with respect to aircraft speed, and the like.
  • x d (x, y, z) destination point for this segment in horizontal coordinates (x, y) and altitude (z).
  • f, fuel level at a point x,(x, y, z) in the flight path.
  • W(t, v, u, x,) a function which describes the winds, in terms of speed v and direction u, at any point in time t and location x,.
  • h(t, x trench X A ) a function which describes the hazards which are extant in the space through which the path lies. The hazards are described in terms of location x, and severity. These hazards can be dynamic aviation weather hazards, such as turbulence and icing, or can be static hazards, such as mountain ranges and restricted airspace.
  • the severity is defined as a function of the aircraft characteristics since the impact of the hazard can be a function of the aircraft.
  • the total cost of traversing this segment is computed by summing the various cost factors.
  • the cost factors can be defined in various ways, depending upon the aircraft and the factors that the user desires to consider in measuring the cost. The number of factors considered determine the computation complexity as well as the sophistication of the cost measurement and optimization.
  • the various cost factors can be weighted to ascribe different emphasis to the various factors, as determined by the user, or the travel path determination system.
  • the weighting factors w noted in the general form of the equation, are presumed to be unity forthe specific example provided herein to reduce the complexity of the computation in this example.
  • weighting factors can themselves be functions of a number of variables, such as type of flight: commercial passenger, commercial freight, military, private pleasure, and the like; or various other factors, such as: instrument rating of pilot, onset of darkness, preferred arrival times at the destination airport, and the like.
  • Total cost (C ⁇ ) w, * time cost (C t ) + w f *fuel cost (C f ) + w n *hazard cost (C h ) or, with unity weighting factors, the equation in the form of the various variables comprises:
  • the time cost is determined by the length of the selected segment and the speed of the aircraft which traverses this segment.
  • the basic time computation is modulated by the effects of hazards which effect the path of travel as well as ambient winds, both factors which change the elapsed time of travel.
  • the aircraft performance factors also effect the time of travel, since the ability of the aircraft to climb/descend as well as operate in various crosswinds and at various altitudes impacts the time cost.
  • time cost computation is that if we assume that the crosswind loss is negligible and the loss in airspeed during a standard ascent, noted above from 5 km altitude to 6 km altitude is from 210 km/hr to 180 km/hr, and the winds are from the South, but change direction to from the Southwest and abate slightly while traversing this segment. Also assume that the change in altitude is accomplished from the starting point for this segment x s , and the climb continues at a standard rate of ascent for this aircraft until the desired cruising altitude is reached.
  • the time cost can be calculated exactly through the analytical solution of an integral equation or through a finite approximation of the integral.
  • the approximation is done by starting at the starting point for this segment x s , at time t s and moving along the path defined by this segment for some small value of Et, then calculating the distance traveled during this time interval Et. This incremental travel computation is repeated for successive intervals of time Et until the destination point x d is reached. The computation performed for each time interval along the length of the segment is performed using the winds that are present during that time interval at that locus on the segment and for the particular ascent/descent profile for this aircraft.
  • the system can compute in a timely manner changes in the heading of the aircraft, such as that shown in Figure 7 to compensate forthe steady wind from the south and the vector direction of the course is illustrated diagrammatically by the heading C in Figure 7.
  • the aircraft is oriented along the heading defined by segment C, but is blown by the ambient winds to the North by an amount given by vector W to thereby reach the point P1 at the end of the 1 minute initial sampling interval.
  • the aircraft changes altitude to 5.3 km and the new location on the path P1 , accounting for the presence of the wind, is the coordinates: (102.75, 79.31 , 5.3).
  • the pilot In order to remain on course, heading forthe destination point x d given by the coordinates (140, 70, 6), the pilot must continue directing the airplane into the wind at the same heading to compensate for its effect on the travel of the aircraft. This process is repeated for the successive time intervals, with the temporal value of the wind being determined for each portion of the segment to correspond to the presence of the aircraft on that portion of the segment, to thereby compute the predicted path taken by the aircraft over this segment. Using these computed portions of the segment, the overall time required to traverse the segment can be determined. Fuel Cost
  • the above computations provide an indication of the time cost to traverse the segment of the travel path.
  • the data generated during that process can be used to determine the fuel cost for the segment.
  • the fuel cost represents the quantity of fuel consumed by the aircraft in traversing each portion of the segment.
  • the fuel consumption measurement is a function of the aircraft performance characteristics at the present altitude; whether the aircraft is climbing, descending, or in level flight; aircraft speed and acceleration; ambient winds; weight of the aircraft, including time-varying fuel level.
  • the fuel consumption determined for each portion of the segment can then be summed to determine the overall fuel cost for the segment of the travel path.
  • Hazard Cost The above computations provide an indication of the time cost and fuel cost to traverse the segment of the travel path.
  • the data generated during these processes can be used to determine the hazard cost for the segment.
  • the hazard cost represents the impact of various hazards on the aircraft as it traverses the segment.
  • a function can be defined which quantifies the effect of the hazards on the aircraft. This can include a measure of the relative comfort or safety of the travel as the aircraft is impacted by the phenomena extant ion the multidimensional space.
  • the overall cost for hazards is determined by summing the individual hazard cost figures for each of the portions of the segment to arrive at a total hazard cost for the segment. Totalizing the Costs
  • the above-computed costs are not all presented in unitless values. It is obvious that the time cost is typically measured in minutes, while the fuel consumption is measured in gallons. To determine the overall cost for this segment, the various cost factors must be converted to equivalent unitless or base unit values. This can be relative values, such as a percentage of a normal value (ex: 120% of standard fuel consumption) or other form of unitless measure. The resultant unitless values can then be summed to arrive at a composite cost for the segment.
  • Single Source Optimized Path The problem of determining the optimal path, given the above-described method of determining costs for each segment in the system, represents the solution of the "shortest path" problem.
  • the "shortest path” measurement corresponds to "least cost” using the identified cost factors.
  • a weighted, directed graph is used with a weight function to map the edges of the directed graph to real-valued weights. The shortest path is therefore the path with the lowest value of the sum of the weights of the path segments.
  • the determination of the shortest path is typically accomplished by use of the technique known as relaxation, wherein an upper bound on the estimated shortest path weight of each node in the directed graph is repeatedly decreased until the upper bound equals the shortest path weight.
  • This technique is well known and simplifies the computational complexity of the problem. Implementations of this algorithm are found in Dijkstra's algorithm and the Bellman- Form algorithm, which are textbook example of such computations. Once this approximation to the optimal path, constrained to pass through graph nodes, is found, a better approximation can be found by iteratively moving the points in the gradient direction until a sufficiently smooth path is found.
  • FIG. 8 Another application is illustrated in Figure 8 where the hazard lies beyond the destination point.
  • the hazard illustrated comprises two thunderstorms TS1 and TS2 which lie past the destination point D.
  • the three- dimensional thunderstorm can be viewed as a two-dimensional phenomena and the possibility of altitude changes constrained.
  • the thunderstorms TS1 and TS2 can then be more effectively (in computational efficiency) tracked.
  • the present automated travel path determination system has the capability to address time varying phenomena, time varying costs and interactive initial conditions to determine an optimum travel path through the multidimensional space.

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Automation & Control Theory (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Traffic Control Systems (AREA)

Abstract

Le système de détermination automatique de la trajectoire d'un véhicule de l'invention calcule une trajectoire pour un véhicule entre un point d'origine et un point de destination en se basant sur les caractéristiques de fonctionnement du véhicule et sur des phénomènes caractéristiques de l'espace multidimensionnel, lesquels phénomènes ont un impact sur le coût de fonctionnement du véhicule. Ce système de détermination de la trajectoire d'un véhicule peut considérer simultanément une pluralité de caractéristiques de fonctionnement de véhicule pour choisir la trajectoire. La trajectoire est optimisée en fonction d'une sélection pondérée d'un certain nombre de facteurs coût, laquelle sélection pondérée représente une combinaison voulue de facteurs coût relatifs au fonctionnement de ce véhicule en particulier. Ce système de détermination de la trajectoire d'un véhicule considère également la nature des phénomènes variant dans le temps qui se produisent à l'intérieur de l'espace multidimensionnel ainsi que l'impact que ces phénomènes variant dans le temps ont sur le véhicule lorsqu'il parcoure la trajectoire. Le système de détermination de la trajectoire d'un véhicule selon la présente invention est utilisé comme système de calcul de la trajectoire de vol des avions, même si les concepts de ce système peuvent s'appliquer à toutes formes de parcours de véhicule.
EP98950653A 1997-09-26 1998-09-23 Systeme de determination d'une trajectoire optimale dans un espace multidimensionnel Withdrawn EP1017964A1 (fr)

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US08/938,246 US6085147A (en) 1997-09-26 1997-09-26 System for determination of optimal travel path in a multidimensional space
US938246 1997-09-26
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